





from math import isclose, sqrt







def   __lowerCamelCase   (				__a  :str       ,	__a  :str       ,	__a  :Any       )						->							tuple[float, float, float]:






		"""simple docstring"""

		A__     =  point_y / 4 / point_x
		A__     =  2 * normal_gradient / (1 + normal_gradient * normal_gradient)
		A__     =  (1 - normal_gradient * normal_gradient) / (
		    1 + normal_gradient * normal_gradient
		)
		A__     =  (sa - ca * incoming_gradient) / (ca + sa * incoming_gradient)

		# to find the next point, solve the simultaeneous equations:
		# y^2 + 4x^2 = 100
		# y - b = m * (x - a)
		# ==> A x^2 + B x + C = 0
		A__     =  outgoing_gradient**2 + 4
		A__     =  2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
		A__     =  (point_y - outgoing_gradient * point_x) ** 2 - 1_0_0

		A__     =  (
		    -linear_term - sqrt(linear_term**2 - 4 * quadratic_term * constant_term       )
		) / (2 * quadratic_term)
		A__     =  (
		    -linear_term + sqrt(linear_term**2 - 4 * quadratic_term * constant_term       )
		) / (2 * quadratic_term)

		# two solutions, one of which is our input point
		A__     =  x_minus if isclose(__lowerCAmelCase       ,	__lowerCAmelCase       ) else x_plus
		A__     =  point_y + outgoing_gradient * (next_x - point_x)

		return next_x, next_y, outgoing_gradient







def   __lowerCamelCase   (				__a  :List[str] = 1.4       ,	__a  :Optional[int] = -9.6       )						->							int:






		"""simple docstring"""

		A__     =  0
		A__     =  first_x_coord
		A__     =  first_y_coord
		A__     =  (10.1 - point_y) / (0.0 - point_x)

		while not (-0.01 <= point_x <= 0.01 and point_y > 0):
				A__ ,     A__ ,     A__     =  next_point(__lowerCAmelCase       ,	__lowerCAmelCase       ,	__lowerCAmelCase       )
				num_reflections += 1

		return num_reflections


if __name__ == "__main__":
					print(F'''{solution() = }''')




"""simple docstring"""


def      lowerCamelCase_					(   __lowerCAmelCase							)				->   list:




						'''simple docstring'''



						if len(__lowerCAmelCase							) <= 1:
												return [tuple(__lowerCAmelCase							)]

						lowerCamelCase__   =[]

						def generate(__lowerCAmelCase  ,       __lowerCAmelCase							):
												lowerCamelCase__   =[0] * n
												res.append(tuple(__lowerCAmelCase							)							)

												lowerCamelCase__   =0
												while i < n:
																		if c[i] < i:
																								if i % 2 == 0:
																														lowerCamelCase__   , lowerCamelCase__   =arr[i], arr[0]
																								else:
																														lowerCamelCase__   , lowerCamelCase__   =arr[i], arr[c[i]]
																								res.append(tuple(__lowerCAmelCase							)							)
																								c[i] += 1
																								lowerCamelCase__   =0
																		else:
																								lowerCamelCase__   =0
																								i += 1

						generate(len(__lowerCAmelCase							)  ,       __lowerCAmelCase							)
						return res


if __name__ == "__main__":
	a				=input('Enter numbers separated by a comma:\n').strip()
	a				=[int(item) for item in user_input.split(',')]
	print(heaps(arr))


